Question: Solve for $x$ and $y$ using elimination. ${6x+2y = 68}$ ${5x+y = 54}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${6x+2y = 68}$ $-10x-2y = -108$ Add the top and bottom equations together. $-4x = -40$ $\dfrac{-4x}{{-4}} = \dfrac{-40}{{-4}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {6x+2y = 68}\thinspace$ to find $y$ ${6}{(10)}{ + 2y = 68}$ $60+2y = 68$ $60{-60} + 2y = 68{-60}$ $2y = 8$ $\dfrac{2y}{{2}} = \dfrac{8}{{2}}$ ${y = 4}$ You can also plug ${x = 10}$ into $\thinspace {5x+y = 54}\thinspace$ and get the same answer for $y$ : ${5}{(10)}{ + y = 54}$ ${y = 4}$